Bernstein center
E934441
The Bernstein center is a fundamental object in the representation theory of p-adic groups that parametrizes and controls the decomposition of smooth representations into blocks.
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
center of a category
ⓘ
mathematical object ⓘ |
| actsOn | category of smooth complex representations of a p-adic reductive group ⓘ |
| appearsIn |
representation theory of GL_n over a p-adic field
ⓘ
representation theory of classical p-adic groups ⓘ |
| context | smooth representations of reductive groups over non-Archimedean local fields ⓘ |
| controls | decomposition of smooth representations into blocks ⓘ |
| definedOver | complex numbers ⓘ |
| describedAs | algebra of central distributions on a p-adic group ⓘ |
| field |
p-adic groups
ⓘ
representation theory ⓘ |
| generalizationOf | center of the Hecke algebra in the Iwahori-spherical case ⓘ |
| hasComponent | primitive idempotents corresponding to inertial equivalence classes ⓘ |
| hasProperty |
functorial in the p-adic group
ⓘ
idempotents correspond to blocks ⓘ |
| introducedBy | Joseph Bernstein NERFINISHED ⓘ |
| is |
algebra of endomorphisms of the identity functor on the category of smooth representations
ⓘ
commutative algebra ⓘ |
| namedAfter | Joseph Bernstein NERFINISHED ⓘ |
| parametrizes |
Bernstein components
ⓘ
blocks of the category of smooth representations ⓘ |
| relatedTo |
Bernstein decomposition
NERFINISHED
ⓘ
Bernstein spectrum NERFINISHED ⓘ Hecke algebras NERFINISHED ⓘ cuspidal support ⓘ local Langlands program NERFINISHED ⓘ parabolic induction ⓘ smooth dual of a p-adic group ⓘ |
| structure | spectrum decomposes into Bernstein components ⓘ |
| usedFor |
block decomposition of representation categories
ⓘ
classification of irreducible smooth representations of p-adic groups ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.